Charles Koch, 78 years old, and his brother, 74-year-old David, are among the nation’s most visible supporters of conservative political causes—a fact that, in many cases, has made their nonpolitical giving a lightning rod for partisan reaction.

Critics say their extensive donations to higher education and health care, among other causes, are tainted by tea party-friendly politics, and rife with hidden strings and agendas. Conservatives call such reactions nonsensical, a product of knee-jerk liberal intolerance.

All of which raises the question: Should nonprofit groups—especially those in a largely liberal city like New York—be concerned with a donor’s political leanings?